Physical items are commonly manufactured by manufacturing systems within production slots. This ensures that physical items having similar constraints that govern their manufacture are appropriately assigned to the same production slot, such that the manufacturing system in question is optimally employed to manufacture the largest number of physical items in the least amount of time at the least amount of cost, while ensuring quality, among other factors. Examples of physical items that are manufactured within production slots in this manner include steel slabs and semiconductor devices, among other types of physical items.
Assigning physical items to be manufactured into production slots can be a difficult problem, however. As such, this problem has been represented as an integer programming (IP) problem that when solved optimally assigns the physical items into the production slots. An IP problem may be defined as the maximization or minimization of a linear objective function under constraints provided by multiple linear inequalities or linear equalities, where the variables expressed within the problem are integers.
Solving IP problems, however, has proven problematic using existing computer hardware where the IP problems are relatively large. For example, the data structure needed to represent such IP problems can require one or more gigabytes of memory. Such memory requirements often exceed the physical memory capacities of common 32-bit computer hardware, and sometimes even exceed the address space of such hardware. As such, more sophisticated and thus more expensive hardware may be required to solve these IP problems, which is disadvantageous.
For these and other reasons, therefore, there is a need for the present invention.